Derive a relation between electric field and potential

Explanation

Consider two equipotential surface A and B with the potential difference dV between them as shown in figure. Let dl be the distance between them and E is the electric field normal to these surfaces.
The work done to move a unit positive charge from B to A against the field E through a displacement dl is
`dw=vec(E).vec(dl)`
= Edl cos 180 (`because theta=180^(@)`, E & dl are antiparallel)
dw = -Edl
This is equal to the potential difference, therefore
`dV=dwimpliesdV=-Edl`
`E=-(dV)/(dl)`